The Dual Bell shape of rocket nozzles is known from the early 60's for providing an altitude compensation. In sea level operation mode of such a Dual Bell nozzle, the inflection point will force the flow to separate from the nozzle wall at the desired location, thus increasing sea level thrust. In altitude operation mode, the plume gradually expands until it finally attaches to the nozzle wall downstream of the inflection point. In reality, however, the Dual Bell nozzle concept has several inherent inefficiencies which reduce its performance from the theoretical optimum.
On the other hand, the function of the rocket nozzle is to expand and accelerate the gas to high velocity, and thereby give thrust efficiency and payload capacity. The thrust efficiency is especially important to upper rocket stages. High thrust performance means high wall temperatures and as a consequence leads to exotic and expensive technologies. The temperature of the walls of a rocket nozzle is dependent on the pressure at the wall and the speed of the flow at the wall.
For controlling the wall temperature of a rocket nozzle, particularly wall portions which are not actively cooled by convection cooling, several techniques have been suggested. First of all, the materials used are to have strength at very high temperatures, which of course is expensive. The nozzle walls also may be covered by coatings that insulate and allow high surface temperatures. This is also expensive. Finally, a cooling film might be used in combination with a continuous nozzle contour.
In the case of using metallic materials, such materials have high cost and a nozzle structure must be built with many joints due to the material availability. The large number of joints, however, lowers the reliability. Alternatively, a ceramic matrix composite material may be used. In this case, the cost is very high and the reliability might be questioned due to little experience for application in rocket nozzles.
Thus, coatings add cost and the potential to lower the steady state temperature is limited. A coating also means reduced reliability due to increased complexity. As to the case of film cooling, there is normally no gas to produce film available for closed cycle engines. Tapping of gas for film cooling purposes would mean serious performance lose.